Question

A randomly selected sample of 100 horse owners found that 72 of them feed two flakes of grass hay in the morning and one flake of alfalfa plus one flake of grass hay in the evening to their horses while the rest feed two flakes of grass hay in the morning and one flake of alfalfa plus oat hay in the evening. The estimated probability that horse owners feed grass hay in the A.M. and alfalfa plus oat hay in the P.M. is:

A. 0.72.
B. 0.50.
C. 0.28.
D. 0.75.

Answer 1

We know that both groups feed grass hay in the morning, so that's 100/100.

First group feeds alfalfa and grass in the evening

Second group feeds alfalfa and oat hay in the evening.

The estimated probability that horse owners feed grass hay the morning (AM) is 100%.

The estimated probability that horse owners feed alfalfa + oat hay in the pm is 28/100 or 28% (C)

Answer 2

The correct answer is B. 0.5

Explanation:

Total number of horse owners =100

72 of the horse owners feed their horses in the morning with

• 2 flakes of grass hay

• 1 flake of alfalfa

72 of the horse owners feed their horses in the evening with

• 1 flake of grass hay in the evening.

28 of the horse owners feed their horses in the morning with

• 2 flakes of grass hay

• 1 flake of alfalfa

28 of the horse owners feed their horses in the evening with

• Oat hay

There are two categories of farmer

P(72) =72/100 =0.72

P(28) = 28/100 = 0.28

P(grass hay in A.M for 72 farmers) = 1/2*72/100 =0.36

P (grass hay in A.M for 28 farmers) =1/2*28/100 = 0.14

P (grass hay in A.M for both farmers) = 0.36 + 0.14 = 0.5

P(alfalfa plus oat hay in P.M for 72 farmers) =0

P(alfalfa plus oat hay in P.M for 28 farmers) =0

P(alfalfa plus oat hay in P.M for both farmers) = 0+ 0 = 0

The estimated probability that horse owners feed grass hay in the AM and alfalfa plus oat hay in the PM is

P (E) = P (grass hay in AM for both farmers) + P(alfalfa plus oat hay in PM for both farmers)

P(E) =0.5 + 0 = 0.5